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Fluctuation theorem for constrained equilibrium systems

T. Gilbert·J. R. Dorfman
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Abstract

We discuss the fluctuation properties of equilibrium chaotic systems with constraints such as iso-kinetic and Nosé-Hoover thermostats. Although the dynamics of these systems does not typically preserve phase-space volumes, the average phase-space contraction rate vanishes, so that the stationary states are smooth. Nevertheless finite-time averages of the phase-space contraction rate have non-trivial fluctuations which we show satisfy a simple version of the Gallavotti-Cohen fluctuation theorem, complementary to the usual fluctuation theorem for non-equilibrium stationary states, and appropriate to constrained equilibrium states. Moreover we show these fluctuations are distributed according to a Gaussian curve for long-enough times. Three different systems are considered here, namely (i) a fluid composed of particles interacting with Lennard-Jones potentials; (ii) a harmonic oscillator with Nosé-Hoover thermostatting; (iii) a simple hyperbolic two-dimensional map.

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T. Gilbert, J. R. Dorfman. 2006-01-19. Fluctuation theorem for constrained equilibrium systems. https://doi.org/10.1103/physreve.73.026121

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